| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2015 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Single period normal approximation - large lambda direct |
| Difficulty | Moderate -0.3 This is a straightforward application of Poisson distribution with standard parts: (a) direct Poisson probability calculation, (b) scaling the rate parameter, and (c) normal approximation for large λ. All three parts follow textbook procedures with no conceptual challenges or novel problem-solving required, making it slightly easier than average. |
| Spec | 2.04d Normal approximation to binomial |
In a survey it is found that barn owls occur randomly at a rate of 9 per 1000 km$^2$.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that in a randomly selected area of 1000 km$^2$ there are at least 10 barn owls. [2]
\item Find the probability that in a randomly selected area of 200 km$^2$ there are exactly 2 barn owls. [3]
\item Using a suitable approximation, find the probability that in a randomly selected area of 50000 km$^2$ there are at least 470 barn owls. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2015 Q1 [11]}}